1. Field of the Invention
The present invention relates to an apparatus and a method for detecting a decrease in the air pressure of a tire of a running vehicle based on the resonance frequency of the tire as well as a program for detecting a decrease in a tire air pressure.
2. Description of the Related Art
Factors for enabling the safe running of an automobile include a tire air pressure. If the air pressure value decreases and is lower than an appropriate value, this causes deteriorated operation stability and fuel efficiency to consequently cause a tire burst. To prevent this, a tire air pressure alarming apparatus (Tire Pressure Monitoring System; TPMS), which is to detect the decrease in a tire air pressure to notify a driver of this decrease to prompt the driver to take an appropriate measure, is an important technique from the viewpoints of environment conservation and the secured safety of the driver.
A conventional alarming apparatus can be classified into two types of the direct detecting-type one (direct TPMS) and the indirect detecting-type one (indirect TPMS). The direct TPMS directly measures a tire air pressure by providing a pressure sensor in a tire wheel. The direct TPMS can accurately detect a decrease in a tire air pressure but requires an exclusive wheel and has a poor fault-tolerance performance in an actual environment for example. Thus, the direct TPMS has disadvantages in technique and cost.
On the other hand, the indirect TPMS uses a method to estimate an air pressure based on the rotation information of a tire. The indirect TPMS can be further classified into the dynamic loaded radius (DLR)-type one and the resonance frequency mechanism (RFM)-type one. The DLR method uses a phenomenon according to which a tire having a reduced pressure collapses during running to cause a reduced dynamic loaded radius and this tire is consequently rotated at a speed higher than that of a tire having a normal pressure. The DLR method compares rotation velocities of four tires to thereby detect a pressure decrease. Since the DLR method can provide a relatively-easy computation using only a wheel rotation velocity signal obtained from a wheel speed sensor, the DLR method has been widely researched mainly for the purpose of detecting the puncture of one wheel. However, this DLR method merely makes a relative comparison among wheel rotation velocities and thus cannot sense a case of four tire simultaneous deflation (natural leakage). Furthermore, this DLR method also has a disadvantage in that this method cannot accurately sense a reduced pressure in all vehicle running statuses because a difference in the wheel speed is also caused by running conditions such as a vehicle turning, acceleration and deceleration, or an uneven load.
On the other hand, the RFM method is a method that uses a fact that a frequency characteristic of a wheel speed signal changes depending on a reduced tire pressure to thereby detect a difference between a reduced tire pressure and a normal tire pressure. In contrast with the DLR method, the RFM method is based on an absolute comparison between a certain value and the normal values of the respective wheels retained in advance. Thus, the RFM method can cope with a case of four tire simultaneous deflation and the RFM has collected attention as a better indirect detecting method. However, the RFM method is disadvantageous in that some running condition causes a strong noise for example and thus an estimated frequency value in a target region is not robust enough with regard to a vehicle speed or a road surface condition for example. The present invention relates to a tire status sensing apparatus based on the RFM method. The following section will describe the basic principle of the RFM method in more detail.
When a vehicle is running, the torsional motion in the front-and-rear direction caused by the force to a tire from the road surface and the front-and-rear motion of the suspension have a coupled resonance. This resonance phenomenon also has an influence on the wheel rotation motion. Thus, a wheel speed signal obtained from a wheel sensor provided in an anti-lock braking system (ABS) also includes the information regarding the resonance phenomenon. The coupled resonance is based on a unique vibration mode caused by the torsional rigidity of a tire. Thus, the excitation status thereof changes depending only on a change in the air pressure constituting the physical characteristic of the tire and rarely depends on a change in the vehicle speed or the road surface. Specifically, when the air pressure decreases, the dynamics of the torsional motion of the tire changes. Thus, when the wheel speed signal is subjected to a frequency analysis for a case where a tire has a reduced pressure, a peak shown by the coupled resonance (resonance peak) appears at a lower frequency-side than in the case where the tire has a normal pressure.
FIG. 3 illustrates the power spectrum obtained by subjecting the respective wheel acceleration signals obtained during a fixed time (which are obtained by calculating time differences among wheel speed signals) to Fast Fourier Transform (FFT) obtained during a fixed time regarding tires attached to a vehicle having a normal air pressure and tires having a pressure reduced by 25% from the normal pressure.
The components in the vicinity of 40 to 50 Hz show the vibration caused when the vibration of the tires in the front-and-rear direction is resonant with the suspension of the vehicle. As can be seen from the components, a change in the internal pressure causes a frequency having a peak value (resonance frequency) to move to the lower-frequency-side. Due to the above-described characteristic, this phenomenon appears independently from the tires, the vehicle type, the running speed, and the road surface condition for example. Thus, this RFM method focuses on this resonance frequency and issues an alarm when it is determined that the resonance frequency is relatively lower than a reference frequency estimated during initialization. In this case, the resonance frequency must be estimated based on a wheel speed signal obtained from ABS. However, an in-vehicle calculator having a limited computational resource has a difficulty in storing required time-series data, thus making it difficult to carry out the FFT frequency analysis. Due to this reason, a conventional method estimates the resonance frequency based on an on-line method as will be described later (See the specification of Japanese Patent No. 3152151, for example).
Since vibration can be described by the 2-order model, a wheel speed signal is subjected to a time-series analysis based on the 2-order autoregressive (AR) model. Specifically, a parameter θ={a1, . . . , aK} in the model represented by the following formula (1) is estimated by the Kalman filter (iterative least squares technique).
                              y          ⁡                      (            t            )                          =                                            ∑                              i                =                1                            K                        ⁢                                          a                i                            ⁢                              y                ⁡                                  (                                      t                    -                    i                                    )                                                              +          ɛ                                    (        1        )            
In this formula, y(t) represents a wheel speed at the time t, ε represents white noise, and K represents the model order. Since the frequency corresponding to the pole of the transfer function representing the AR model is estimated as a resonance frequency, the resonance frequency can be accurately obtained if a resonance peak is correctly extracted by the model.
However, the conventional method according to the specification of Japanese Patent No. 3152151 has a disadvantage as described below. For example, when a wheel acceleration signal obtained from a vehicle running at a high speed (e.g., 80 km per hour or more) is subjected to a time-series analysis based on a conventional 2-order model, the vertical vibration of tires increasing in proportion to the speed causes an increase in the gain in the vicinity of 80 to 100 Hz, thus failing to correctly extract a target resonance peak. Specifically, under the circumstance where a wheel acceleration signal given as data includes a large amount of information regarding vibrations other than the torsional vibration, only a desired 2-order model cannot be selectively extracted through the above-described simple time-series model. Consequently, a plurality of factors are described evenly. FIG. 4 illustrates the phenomenon as described above. FIG. 4 shows the result of subjecting wheel acceleration signals obtained in two minutes to a FFT frequency analysis, to a time-series analysis based on a 2-order AR model, and to a time-series analysis based on a 20-order AR model. In FIG. 4, the horizontal axis represents the frequency (Hz) and the vertical axis represents the signal strength (dB). A component considered to be caused by the vertical vibration of tires for example is included in a high-frequency component of 80 Hz or more. Thus, it is understood that the resonance frequency estimated by the time-series analysis based on the 2-order AR model is significantly different from the resonance frequency shown by the FFT frequency analysis. When the estimated value depends on an external factor as described above, a reference frequency obtained by initialization under a certain condition is not universal as a reference value for the determination of the abnormality in a tire (reduction in tire pressure). Thus, this reference frequency cannot be expected to accurately operate under an actual environment in which various running conditions are anticipated.
To prevent this, the present applicant has suggested a method of solving this problem caused by the mismatch between models by increasing the number of orders of a model (Japanese Patent Application No. 2008-129055). Specifically, the difficulty in selectively extracting only a desired 2-order model from various pieces of information included in a wheel speed signal is solved by the use of a model having a higher order.
According to this method, the model can have an improved expression capability. Thus, other factors which cannot be expressed by a low-order model can be all described, thus improving the dependency of an estimated value on an external factor. FIG. 4 shows the result of the time-series analysis based on a 20-order AR model. By the increased order, the same value as that of the resonance frequency shown by the FFT frequency analysis can be obtained.
Although the time-series analysis based on a high-order model can correctly identify a peak position, the high order makes it difficult to calculate the pole of the transfer function. In other words, it is difficult to calculate a frequency having a peak value (resonance frequency). To solve this, the above suggestion uses a dimension reduction method with regard to the result of a high-order estimate to thereby change the model to a 2-order model without damaging the estimate accuracy, thereby calculating the resonance frequency.
However, this method has the following two disadvantages. First, the reduction of the order of a model is performed with regard to a fixed frequency range including a resonance peak. However, when other peaks caused by noise for example are in the vicinity of the resonance peak, these peaks are described as a single 2-order model. This consequently causes a case where an estimated resonance frequency value may not be correctly calculated due to the influence by other peaks. FIG. 5 shows an example where this disadvantage appears. FIG. 5 shows the result of subjecting wheel acceleration signals obtained in two minutes to a FFT frequency analysis, a time-series analysis based on a high-order model, and an analysis of a 2-order model obtained by subjecting the result of a time-series analysis based on a high-order model to dimension reduction to reduce the order. In FIG. 5, the horizontal axis represents a frequency (Hz) and the vertical axis represents a signal strength (dB). In this example, the time-series analysis based on the high-order model shows a resonance peak in the vicinity of 48 Hz and also shows an increase in the vicinity of 41 Hz close to 48 Hz. Thus, when the original model is subjected to dimension reduction to provide a 2-order model, the resonance peak position is slightly displaced due to this increase. Although this displacement is not high as that shown in FIG. 4, this displacement is not desirable from the requirement for realizing a high accuracy for detecting an abnormality. On the other hand, if the gain to an arbitrary frequency can be calculated based on the analysis result by a high-order model, a frequency having the maximum gain in frequencies in the vicinity of a resonance peak can be assumed as a resonance frequency. However, since the calculation of the gain of a discrete signal generally requires a value of a nonlinear function, a direct use of this approach in an in-vehicle environment causes a high cost and thus is not realistic.
Secondly, in order to reduce the dimension in the above-suggested method, the filtering by a bandpass filter allowing a fixed frequency range including a resonance peak to pass therethrough must be performed as a pre-processing in order to minimize the first disadvantage. However, since a different tire type has a different resonance frequency, the range within which the filter can be used changes. When the type of tires attached to a vehicle is known in advance, the filter may be used within a determined range. However, such a circumstance cannot be expected in an actual case. Thus, a processing for dynamically changing the application range of the filter is required by finding the type of tires during initialization for example.
However, such a processing is theoretically difficult and is also burdensome. On the other hand, if such a processing is not provided, the only option is to unnecessarily expand the application range of the bandpass filter, thus further consequently complicating the first disadvantage.